Question

$x^2+5x+6$ can be factorised as

• A. $(x+2)(x+3)$
• B. $(x+2)(x-3)$
• C. $(x-2)(x-3)$
• D. $(x-2)(x+3)$

Answer 1

The correct option is A $(x+2)(x+3)$

If we compare the given expression with $x^2+(a+b)x+ab,$ then;

$a+b=5\cdots \left(i\right)\&ab=6\cdots \left(ii\right)$

Now, we will try putting the values for $a\&b$ for which they satisfy the above two equations.

After checking for a few combinations, we can tell $a=2,b=3$ is one of the possible desired combinations as it satisfies both the equations simultaneously.
$x^2+5x+6=x^2+(2+3)x+6=x^2+2x+3x+6=x(x+2)+3(x+2)\Rightarrow x^2+5x+6=(x+2)(x+3)$